Finite Group Databasebeta

← #21436122

Subgroups — #21436122

Order 7552.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838093C211yesmaximal, characteristic, complemented
2D4×D236C211yesmaximal, characteristic
3#16837767C211yesmaximal, characteristic, complemented
4#16837729C211yesmaximal, characteristic, complemented
5#16837717C211yesmaximal, characteristic, complemented
6#16837702C211yesmaximal, characteristic, complemented
7#16837651C211yesmaximal, characteristic, complemented
8#16837634C211yesmaximal, characteristic, complemented
9#16837602C211yesmaximal, characteristic, complemented
10#16837551C211yesmaximal, characteristic, complemented
11#16837551C211yesmaximal, characteristic, complemented
12#16837475C211yesmaximal, characteristic, complemented
13#16837405C211yesmaximal, characteristic, complemented
14#102×D59C211yesmaximal, characteristic, complemented
15C59×#440C211yesmaximal, characteristic, complemented
16C22×D236—21no—
17C2×D4×D59C2211yescharacteristic
18C2×D4×D59C2211yescharacteristic
19C2×#11745671C2211yescharacteristic, complemented
20C2×#11745671C2211yescharacteristic, complemented
21C2×#11745659C2211yescharacteristic, complemented
22C2×C8×D59C2211yescharacteristic, complemented
23#14273724C2211yescharacteristic
24#14273721—21no—
25#14273719C2211yescharacteristic, complemented
26#14273717—21no—
27#14273712—21no—
28#14273703C2211yescharacteristic, complemented
29#14273703C2211yescharacteristic, complemented
30#14273702C2211yescharacteristic
31#14273702C2211yescharacteristic
32#14273701—21no—
33#14273697—21no—
34#14273697—21no—
35C4×D236C2211yescharacteristic
36#14273685C2211yescharacteristic, complemented
37#14273684—21no—
38C4⋊C4×D59C2211yescharacteristic, complemented
39#14273660C2211yescharacteristic, complemented
40#14273658C2211yescharacteristic, complemented
41C4⋊(C59⋊C8)C2211yescharacteristic, complemented
42#14273649C2211yescharacteristic, complemented
43#14273649C2211yescharacteristic, complemented
44#14273649C2211yescharacteristic, complemented
45#14273649C2211yescharacteristic, complemented
46#14273648C2211yescharacteristic
47#14273648C2211yescharacteristic
48#14273647C2211yescharacteristic, complemented
49#14273647C2211yescharacteristic, complemented
50(C2×D59)⋊C8C2211yescharacteristic, complemented
51(C2×D59)⋊C8C2211yescharacteristic, complemented
52C2×SD16×C59C2211yescharacteristic
53C4×Q8×C59C2211yescharacteristic, complemented
54C4×D4×C59C2211yescharacteristic
55#107×C59C2211yescharacteristic, complemented
56#103×C59C2211yescharacteristic, complemented
57#102×C59C2211yescharacteristic
58#97×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C23×D59—21no—
61C2×Q8×C59C2311yescharacteristic
62C2×D4×C59C2311yescharacteristic
63C22×C4×C59—21no—
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66D4×D59—22no—
67D4×D59—22no—
68D4×D59—41no—
69D4×D59—41no—
70C2×D236—21no—
71C2×D236—21no—
72C2×D236—21no—
73C2×D236—21no—
74C2×D236—44no—
75C2×D236D411yescharacteristic
76C2×D236C2311yescharacteristic
77C2×D236C2311yescharacteristic
78C2×C4×D59—21no—
79C2×C4×D59C2311yescharacteristic
80C2×C4×D59C2311yescharacteristic
81SD16×C59—22no—
82C2×C8×C59C2311yescharacteristic
83C2×C8×C59C2311yescharacteristic
84C4⋊C4×C59—21no—
85C4⋊C4×C59C2311yescharacteristic
86C4⋊C4×C59C2311yescharacteristic
87C22⋊C4×C59—21no—
88C42×C59—21no—
89C42×C59C2311yescharacteristic
90#11745671—41no—
91#11745671—41no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4D411yescharacteristic
98(C2×D59)⋊C4D411yescharacteristic
99C4⋊Dic59D411yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106Dic59⋊C4—21no—
107C4×Dic59—21no—
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110#11745659—41no—
111C8×D59—41no—
112C23×C59—21no—
113C22×D59—21no—
114C22×D59—21no—
115C22×D59—42no—
116C22×D59—42no—
117C22×D59—42no—
118C22×D59—42no—
119C22×D59—81no—
120C22×D59—81no—
121C22×D59C2×D411yescharacteristic
122C22×D59C2×D411yescharacteristic
123Q8×C59—21no—
124Q8×C59—21no—
125D4×C59—21no—
126D4×C59#4112yes—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—42no—
131C2×C4×C59C2×D411yescharacteristic
132C2×C4×C59C2×D411yescharacteristic
133C2×C4×C59C2411yescharacteristic
134C22⋊D59—42no—
135C22⋊D59—42no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59C2×D411yescharacteristic
139C2×Dic59C2×D411yescharacteristic
140D236—22no—
141D236—21no—
142D236—21no—
143D236—21no—
144D236—21no—
145D236—42no—
146D236—42no—
147D236—42no—
148D236—81no—
149C4×D59—21no—
150C4×D59—21no—
151C4×D59—21no—
152C4×D59—21no—
153C4×D59—42no—
154C8×C59—21no—
155C8×C59—21no—
156C59⋊C8—21no—
157C59⋊C8—21no—
158C22×C59—22no—
159C22×C59—41no—
160C22×C59—41no—
161C22×C59C22×D411yescharacteristic
162C2×D59—21no—
163C2×D59—21no—
164C2×D59—21no—
165C2×D59—21no—
166C2×D59—21no—
167C2×D59—41no—
168C2×D59—41no—
169C2×D59—41no—
170C2×D59—41no—
171C2×D59—41no—
172C2×D59—41no—
173C2×D59—84no—
174C2×D59—84no—
175C2×D59AGL(1,ℤ/8)12yes—
176C4×C59—21no—
177C4×C59—21no—
178C4×C59—41no—
179C4×C59—41no—
180C4×C59—41no—
181C4×C59C2×#4111yescharacteristic
182C4×C59H(5,𝔽2)11yescharacteristic
183Dic59—21no—
184Dic59—21no—
185Dic59—41no—
186Dic59—41no—
187#3310—591nomaximal, Sylow
188C2×C59—42no—
189C2×C59#54611yescharacteristic
190C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C59#57711yescharacteristic
192D59—22no—
193D59—41no—
194D59—81no—
195D59—81no—
196#552—591no—
197D42—591no—
198#490—591no—
199#482—591no—
200#480—591no—
201#478—591no—
202#468—591no—
203#465—591no—
204#460—591no—
205#450—591no—
206#450—591no—
207#440D5911yescharacteristic, complemented
208#435—591no—
209#418—591no—
210C2×#102—591no—
211C59#331011yescharacteristic, complemented, Sylow
212C22×D4—591no—
213C22×D4—591no—
214C22×D4—1181no—
215C2×SD16—591no—
216C2×SD16—591no—
217C2×SD16C2×D5911yescharacteristic
218C2×M16—591no—
219C22×C8—591no—
220#127—591no—
221#126—1181no—
222#125—591no—
223#125—1181no—
224#123—1181no—
225C22⋊Q8—591no—
226C22⋊Q8—591no—
227#121—591no—
228#121—591no—
229#121—1181no—
230#120—1181no—
231#120—1181no—
232C4×Q8C2×D5911yescharacteristic, complemented
233C4×D4—591no—
234C4×D4C2×D5911yescharacteristic
235#117—591no—
236#117—1181no—
237C2×C4⋊C4—591no—
238#107—591no—
239#107C2×D5911yescharacteristic, complemented
240#106—591no—
241C4⋊C8—591no—
242#103C2×D5911yescharacteristic, complemented
243#102—591no—
244#102—591no—
245#102—591no—
246#102—591no—
247#102—591no—
248#102—591no—
249#102—591no—
250#102—591no—
251#102C2×D5911yescharacteristic
252C22⋊C8—591no—
253C22⋊C8—591no—
254#97C2×D5911yescharacteristic, complemented
255C24—1181no—
256C24—1181no—
257C2×Q8C22×D5911yescharacteristic
258C2×D4—591no—
259C2×D4—591no—
260C2×D4—591no—
261C2×D4—1181no—
262C2×D4—1181no—
263C2×D4—1181no—
264C2×D4—1181no—
265C2×D4—1182no—
266C2×D4—1182no—
267C2×D4—1181no—
268C2×D4—1181no—
269C2×D4—2364no—
270C2×D4—2361no—
271C2×D4—2361no—
272C2×D4C22×D5911yescharacteristic
273C22×C4—21no—
274C22×C4—591no—
275C22×C4—591no—
276C22×C4—1181no—
277SD16—22no—
278SD16—2361no—
279SD16—2361no—
280M16—2361no—
281C2×C8—591no—
282C2×C8—591no—
283C2×C8—2361no—
284C2×C8C22×D5911yescharacteristic
285C2×C8C22×D5911yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—591no—
288C4⋊C4—591no—
289C4⋊C4—591no—
290C4⋊C4—1181no—
291C4⋊C4—1181no—
292C4⋊C4—1181no—
293C4⋊C4—1181no—
294C4⋊C4—1181no—
295C4⋊C4C22×D5911yescharacteristic
296C4⋊C4C22×D5911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—591no—
299C22⋊C4—591no—
300C22⋊C4—1181no—
301C22⋊C4—1181no—
302C22⋊C4—1181no—
303C22⋊C4—1181no—
304C22⋊C4—1181no—
305C42—21no—
306C42—1181no—
307C42C22×D5911yescharacteristic
308C23—21no—
309C23—591no—
310C23—591no—
311C23—1181no—
312C23—1181no—
313C23—4721no—
314C23—4721no—
315C23—2362no—
316C23—2362no—
317C23—2362no—
318C23—2362no—
319Q8—21no—
320Q8—21no—
321D4—21no—
322D4—1182no—
323D4—1181no—
324D4—1181no—
325D4—1181no—
326D4—1181no—
327D4—4721no—
328D4—2362no—
329D4—2362no—
330D4—2362no—
331D4—2362no—
332D4—2362no—
333D4#1174568512yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—591no—
339C2×C4—591no—
340C2×C4—1181no—
341C2×C4—1181no—
342C2×C4—1181no—
343C2×C4—1181no—
344C2×C4—1181no—
345C2×C4—1181no—
346C2×C4—2362no—
347C2×C4D4×D5911yescharacteristic
348C2×C4D4×D5911yescharacteristic
349C2×C4C23×D5911yescharacteristic
350C8—21no—
351C8—21no—
352C8—1181no—
353C8—1181no—
354C22—22no—
355C22—41no—
356C22—41no—
357C22—592no—
358C22—1181no—
359C22—1181no—
360C22—1181no—
361C22—1181no—
362C22—1181no—
363C22—4724no—
364C22—4724no—
365C22—2361no—
366C22—2361no—
367C22—2361no—
368C22—2361no—
369C22—2361no—
370C22—2361no—
371C22C2×D4×D5911yescharacteristic
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—1181no—
378C4—1181no—
379C4—2361no—
380C4—2361no—
381C4C2×#1174568511yescharacteristic
382C4#1427377311yescharacteristic
383C2—42no—
384C2—1182no—
385C2—4721no—
386C2—4721no—
387C2—2361no—
388C2#1683804811yescharacteristic
389C2AGL(1,ℤ/8)×D5911yescharacteristic
390C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#440C2
socleC22×C59C22×D4
hypercenter#440D59
hypocenterC59#3310
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #16838093C2semidirect
3. #16837767C2semidirect
4. #16837729C2semidirect
5. #16837717C2semidirect
6. #16837702C2semidirect
7. #16837651C2semidirect
8. #16837634C2semidirect
9. #16837602C2semidirect
10. #16837551C2semidirect
11. #16837551C2semidirect
12. #16837475C2semidirect
13. #16837405C2semidirect
14. #102×D59C2semidirect
15. C59×#440C2semidirect
19. C2×#11745671C22semidirect
20. C2×#11745671C22semidirect
21. C2×#11745659C22semidirect
22. C2×C8×D59C22semidirect
25. #14273719C22semidirect
28. #14273703C22semidirect
29. #14273703C22semidirect
36. #14273685C22semidirect
38. C4⋊C4×D59C22semidirect
39. #14273660C22semidirect
40. #14273658C22semidirect
41. C4⋊(C59⋊C8)C22semidirect
42. #14273649C22semidirect
43. #14273649C22semidirect
44. #14273649C22semidirect
45. #14273649C22semidirect
48. #14273647C22semidirect
49. #14273647C22semidirect
50. (C2×D59)⋊C8C22semidirect
51. (C2×D59)⋊C8C22semidirect
53. C4×Q8×C59C22semidirect
55. #107×C59C22semidirect
56. #103×C59C22semidirect
58. #97×C59C22semidirect
207. #440D59semidirect
211. C59#3310semidirect
232. C4×Q8C2×D59semidirect
239. #107C2×D59semidirect
242. #103C2×D59semidirect
254. #97C2×D59semidirect